Finite Group Databasebeta

← #10794876

Subgroups — #10794876

Order 768.

1330 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5750C211yesmaximal, characteristic
2C2×#4893C211yesmaximal, characteristic, complemented
3C2×#4861C211yesmaximal, characteristic, complemented
4#78881C211yesmaximal, characteristic
5D3×#417C211yesmaximal, characteristic
6C3×#1815C211yesmaximal, characteristic, complemented
7#72016C211yesmaximal, characteristic, complemented
8#70721C211yesmaximal, characteristic, complemented
9#70592C211yesmaximal, characteristic, complemented
10#70300C211yesmaximal, characteristic, complemented
11#70299C211yesmaximal, characteristic, complemented
12#69001C211yesmaximal, characteristic, complemented
13#69000C211yesmaximal, characteristic, complemented
14#68989C211yesmaximal, characteristic, complemented
15D3×#343C211yesmaximal, characteristic, complemented
16#20679—31nomaximal, Sylow
17C2×D3×#41C2211yescharacteristic
18C2×C3×#131C2211yescharacteristic
19C2×#948C2211yescharacteristic
20#5750—24no—
21#5750C418yescomplemented
22C2×#907—21no—
23C2×#907C2211yescharacteristic
24C2×D3×M16—21no—
25C2×D3×M16C2211yescharacteristic
26C2×D3×M16C2211yescharacteristic
27C2×D3×M16C2211yescharacteristic
28C2×#901—21no—
29C2×#901C2211yescharacteristic
30C22×ΓL(1,𝔽25)—21no—
31C22×ΓL(1,𝔽25)C2211yescharacteristic
32C2×#892C2211yescharacteristic
33C2×D3×C4⋊C4C2211yescharacteristic
34C2×C3×#108C2211yescharacteristic, complemented
35C2×C3×#106C2211yescharacteristic, complemented
36C3×#417C2211yescharacteristic
37C3×#417C2211yescharacteristic
38#5232C2211yescharacteristic
39#5232C2211yescharacteristic
40#5133C2211yescharacteristic
41#5133C2211yescharacteristic
42C2×#822C2211yescharacteristic, complemented
43C2×#822C2211yescharacteristic, complemented
44C2×#819C2211yescharacteristic, complemented
45C2×#818C2211yescharacteristic, complemented
46#4966C2211yescharacteristic
47#4966C2211yescharacteristic
48C2×#808C2211yescharacteristic, complemented
49C2×#807C2211yescharacteristic, complemented
50#4893—24no—
51#4861—21no—
52#4861—21no—
53#4861—21no—
54#4861—21no—
55#4804—21no—
56#4803—21no—
57#4802—21no—
58D3×#103—21no—
59#4772—21no—
60#4771—21no—
61#4770—21no—
62D3×#102—21no—
63C3×#343C2211yescharacteristic, complemented
64C3×#343C2211yescharacteristic, complemented
65#4554C2211yescharacteristic, complemented
66#4554C2211yescharacteristic, complemented
67#4554C2211yescharacteristic, complemented
68#4554C2211yescharacteristic, complemented
69#4530C2211yescharacteristic, complemented
70#4530C2211yescharacteristic, complemented
71C2×#568—31no—
72C2×#430—31no—
73C2×#428—31no—
74#2896—31no—
75C2×#417—31no—
76#1816—31no—
77#1816—31no—
78#1816—31no—
79#1816—31no—
80#1815—31no—
81#1815—31no—
82#1815—31no—
83#1815D311yescharacteristic, complemented
84#1742—31no—
85C2×#343—31no—
86C2×C3×#41C2311yescharacteristic
87D3×#41—22no—
88D3×#41—22no—
89D3×#41C2×C414yes—
90D3×#41Q814yes—
91C2×#239D411yescharacteristic
92C2×D3×Q8D411yescharacteristic
93C2×#237—21no—
94C2×#237D411yescharacteristic
95C2×D3×D4—21no—
96C2×D3×D4D411yescharacteristic
97C2×#235—21no—
98C2×#235C2311yescharacteristic
99C22×C4×D3—21no—
100C22×C4×D3—21no—
101C22×C4×D3C2311yescharacteristic
102C3×#131—22no—
103C3×#131C2×C414yescomplemented
104C2×C3×M16—21no—
105C2×C3×M16C2311yescharacteristic
106C2×C3×M16C2311yescharacteristic
107C2×C3×M16C2311yescharacteristic
108C22×C3×C8—21no—
109C22×C3×C8C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112#948—22no—
113#948C2×C414yescomplemented
114C2×(C2×D3)⋊C4—21no—
115C2×C4⋊Dic3C2311yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117C2×Dic3⋊C4—21no—
118C2×C4×Dic3—21no—
119C2×#208—21no—
120C2×#208C2311yescharacteristic
121C2×#208C2311yescharacteristic
122C2×#208C2311yescharacteristic
123C22×C3⋊C8—21no—
124C22×C3⋊C8C2311yescharacteristic
125#907—22no—
126#907—28no—
127#907C2×C414yescomplemented
128D3×M16—22no—
129D3×M16—28no—
130D3×M16—22no—
131D3×M16—22no—
132D3×M16—22no—
133D3×M16—22no—
134D3×M16C2×C414yes—
135#901—22no—
136#901—28no—
137#901C2×C414yescomplemented
138C2×ΓL(1,𝔽25)—21no—
139C2×ΓL(1,𝔽25)—21no—
140C2×ΓL(1,𝔽25)—21no—
141C2×ΓL(1,𝔽25)—28no—
142C2×ΓL(1,𝔽25)—21no—
143C2×ΓL(1,𝔽25)—21no—
144C2×ΓL(1,𝔽25)C2×C414yes—
145C2×ΓL(1,𝔽25)D414yes—
146C2×ΓL(1,𝔽25)D411yescharacteristic
147C2×ΓL(1,𝔽25)D411yescharacteristic
148C2×ΓL(1,𝔽25)D411yescharacteristic
149C2×ΓL(1,𝔽25)D411yescharacteristic
150C2×D3×C8—21no—
151C2×D3×C8—21no—
152C2×D3×C8—21no—
153C2×D3×C8—21no—
154C2×D3×C8—21no—
155#892—21no—
156#892—21no—
157#892—21no—
158#892—21no—
159D3×C4⋊C4—21no—
160D3×C4⋊C4—21no—
161D3×C4⋊C4—21no—
162D3×C4⋊C4—21no—
163C3×#108—22no—
164C3×#106—21no—
165C3×#106—21no—
166C3×#103—21no—
167C3×#103—21no—
168C3×#102—21no—
169C3×#102—21no—
170#835—21no—
171#835—21no—
172#832—21no—
173#832—21no—
174#822—22no—
175#822—22no—
176#821—21no—
177#821—21no—
178#819—22no—
179#818—21no—
180#818—21no—
181#816—21no—
182#816—21no—
183#810—21no—
184#810—21no—
185#809—21no—
186#809—21no—
187#808—21no—
188#808—21no—
189#807—21no—
190#807—21no—
191C22×#41—31no—
192#568—38no—
193#568—64no—
194C2×#131—31no—
195C2×#131—31no—
196C2×#131—31no—
197C2×#131—61no—
198C2×#131—61no—
199C2×#131C2×D311yescharacteristic
200C22×M16—31no—
201C22×M16—31no—
202C22×M16—31no—
203C22×M16—31no—
204C22×M16—61no—
205C22×M16—61no—
206C2×#117—31no—
207C22×C4⋊C4—31no—
208#430—64no—
209C2×#108—31no—
210C2×#108—31no—
211C2×#108—31no—
212C2×#108C2×D311yescharacteristic, complemented
213#428—61no—
214#428—61no—
215#428—61no—
216#428—61no—
217C2×#107—31no—
218C2×#107—31no—
219C2×#106—31no—
220C2×#106C2×D311yescharacteristic, complemented
221#419—61no—
222#418—61no—
223#417—31no—
224#417—31no—
225#417—31no—
226#417—31no—
227#417—31no—
228#417—31no—
229#417—61no—
230#417—61no—
231#417C2×D311yescharacteristic
232#417C2×D311yescharacteristic
233#416—61no—
234#416—61no—
235C2×#103—61no—
236C2×#102—61no—
237#343—31no—
238#343—31no—
239#343—31no—
240#343—31no—
241#343—31no—
242#343—31no—
243#343C2×D311yescharacteristic, complemented
244#343C2×D311yescharacteristic, complemented
245C23×D3—21no—
246C23×D3#4111yescharacteristic
247C3×#41—21no—
248C3×#41—21no—
249C3×#41C22×C412yes—
250C3×#41C2×Q812yes—
251C2×C3×Q8C2×D411yescharacteristic
252C2×C3×D4—21no—
253C2×C3×D4C2×D411yescharacteristic
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4C2411yescharacteristic
258C2×#67—21no—
259C2×#67—21no—
260C2×#67—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3#4111yescharacteristic
265#239—22no—
266#239C4⋊C414yes—
267D3×Q8—22no—
268D3×Q8C4⋊C414yes—
269#237—24no—
270#237—24no—
271#237—22no—
272#237C4⋊C414yes—
273D3×D4—24no—
274D3×D4—24no—
275D3×D4—22no—
276D3×D4C4⋊C414yes—
277#235—21no—
278#235—21no—
279#235—24no—
280#235—24no—
281#235C22×C412yes—
282#235C2×Q812yes—
283C2×D12—21no—
284C2×D12C2×D411yescharacteristic
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—24no—
289C2×C4×D3—24no—
290C2×C4×D3—41no—
291C2×C4×D3—41no—
292C2×C4×D3—82no—
293C2×C4×D3C22×C412yes—
294C2×C4×D3C2×D412yes—
295C2×C4×D3C2×D411yescharacteristic
296C2×C4×D3C2×D411yescharacteristic
297C2×C4×D3C2×D411yescharacteristic
298C2×C4×D3C2×D411yescharacteristic
299C2×C4×D3C2×Q812yes—
300C2×C4×D3#4112yes—
301C2×Dic6—21no—
302C2×Dic6C2×D411yescharacteristic
303C3×M16—21no—
304C3×M16—24no—
305C3×M16—21no—
306C3×M16—21no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16C22×C412yes—
310C2×C3×C8—21no—
311C2×C3×C8—24no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8C22×C412yes—
315C2×C3×C8C2×D411yescharacteristic
316C2×C3×C8C2×D411yescharacteristic
317C2×C3×C8C2×D412yes—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322(C2×D3)⋊C4—41no—
323(C2×D3)⋊C4—41no—
324C4⋊Dic3—21no—
325C4⋊Dic3—21no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328Dic3⋊C4—41no—
329Dic3⋊C4—41no—
330C4×Dic3—41no—
331C4×Dic3—41no—
332#208—21no—
333#208—24no—
334#208—21no—
335#208—21no—
336#208—21no—
337#208—21no—
338#208C22×C412yes—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—24no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8C22×C412yes—
344C2×C3⋊C8C2×D411yescharacteristic
345C2×C3⋊C8C2×D411yescharacteristic
346C2×C3⋊C8C2×D412yes—
347ΓL(1,𝔽25)—24no—
348ΓL(1,𝔽25)—24no—
349ΓL(1,𝔽25)—24no—
350ΓL(1,𝔽25)—42no—
351ΓL(1,𝔽25)—42no—
352ΓL(1,𝔽25)C22⋊C414yes—
353ΓL(1,𝔽25)C22⋊C414yes—
354ΓL(1,𝔽25)C22⋊C414yes—
355ΓL(1,𝔽25)C22⋊C414yes—
356D3×C8—24no—
357D3×C8—24no—
358D3×C8—24no—
359D3×C8—42no—
360D3×C8—42no—
361C2×#41—34no—
362C2×#41—34no—
363C2×#41—31no—
364C2×#41—31no—
365C2×#41—31no—
366C2×#41—61no—
367C2×#41—61no—
368C2×#41—62no—
369C2×#41—62no—
370C2×#41C22×D311yescharacteristic
371C22×Q8—31no—
372C22×D4—31no—
373C22×D4—61no—
374C23×C4—31no—
375C23×C4—61no—
376C23×C4—61no—
377#131—22no—
378#131—34no—
379#131—34no—
380#131—34no—
381#131—68no—
382#131—62no—
383#131—62no—
384#131—68no—
385#131—62no—
386#131C4×D314yescomplemented
387C2×M16—21no—
388C2×M16—34no—
389C2×M16—31no—
390C2×M16—31no—
391C2×M16—31no—
392C2×M16—31no—
393C2×M16—34no—
394C2×M16—31no—
395C2×M16—34no—
396C2×M16—31no—
397C2×M16—31no—
398C2×M16—61no—
399C2×M16—68no—
400C2×M16—61no—
401C2×M16—61no—
402C2×M16—61no—
403C2×M16—61no—
404C2×M16—68no—
405C2×M16—62no—
406C2×M16—61no—
407C2×M16—62no—
408C2×M16—62no—
409C2×M16—62no—
410C2×M16—62no—
411C2×M16C22×D311yescharacteristic
412C2×M16C22×D311yescharacteristic
413C2×M16C22×D311yescharacteristic
414C22×C8—21no—
415C22×C8—31no—
416C22×C8—61no—
417C22×C8—61no—
418C22×C8—61no—
419C22×C8—61no—
420C22×C8—61no—
421C22×C8—61no—
422C22×C8C22×D311yescharacteristic
423#117—61no—
424#117—61no—
425#117—61no—
426#117—61no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—61no—
430C2×C4⋊C4—61no—
431C2×C4⋊C4—61no—
432C2×C4⋊C4—61no—
433C2×C4⋊C4—61no—
434C2×C4⋊C4C22×D311yescharacteristic
435C2×C4⋊C4C22×D311yescharacteristic
436C2×C22⋊C4—61no—
437C2×C42—61no—
438#108—22no—
439#108—62no—
440#108—62no—
441#108—62no—
442#107—61no—
443#107—61no—
444#107—61no—
445#107—61no—
446#106—21no—
447#106—21no—
448#106—61no—
449#106—61no—
450#103—21no—
451#103—21no—
452#103—61no—
453#103—61no—
454#103—61no—
455#103—61no—
456#103—61no—
457#103—61no—
458#102—21no—
459#102—21no—
460#102—61no—
461#102—61no—
462#102—61no—
463#102—61no—
464#102—61no—
465#102—61no—
466C23×C3—21no—
467C23×C3C2×#4111yescharacteristic
468C22×D3—21no—
469C22×D3—24no—
470C22×D3—41no—
471C22×D3—41no—
472C22×D3—81no—
473C22×D3—81no—
474C22×D3#11712yes—
475C22×D3#12111yescharacteristic
476C22×D3#12111yescharacteristic
477C22×D3C22⋊Q812yes—
478C3×Q8—21no—
479C3×Q8C2×C4⋊C412yes—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—21no—
483C3×D4C2×C4⋊C412yes—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—81no—
490C2×C3×C4—81no—
491C2×C3×C4C23×C411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×Q811yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497#67—22no—
498#67—22no—
499#67—24no—
500#67—24no—
501C2×Dic3—21no—
502C2×Dic3—24no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—81no—
506C2×Dic3—81no—
507C2×Dic3#11712yes—
508C2×Dic3#12111yescharacteristic
509C2×Dic3#12111yescharacteristic
510C2×Dic3C22⋊Q812yes—
511D12—24no—
512D12—21no—
513D12C2×C4⋊C412yes—
514C4×D3—24no—
515C4×D3—22no—
516C4×D3—22no—
517C4×D3—24no—
518C4×D3—82no—
519C4×D3—82no—
520C4×D3C2×C22⋊C412yes—
521C4×D3C2×C22⋊C412yes—
522C4×D3C2×C4⋊C412yes—
523C4×D3C2×C4⋊C412yes—
524C4×D3#12112yes—
525C4×D3#12112yes—
526C4×D3C22⋊Q812yes—
527C4×D3C22⋊Q812yes—
528Dic6—21no—
529Dic6—24no—
530Dic6C2×C4⋊C412yes—
531C3×C8—22no—
532C3×C8—41no—
533C3×C8—41no—
534C3×C8C2×C22⋊C412yes—
535C3×C8C2×C22⋊C412yes—
536C3⋊C8—22no—
537C3⋊C8—41no—
538C3⋊C8—41no—
539C3⋊C8C2×C22⋊C412yes—
540C3⋊C8C2×C22⋊C412yes—
541C24—31no—
542C24—61no—
543#41—21no—
544#41—21no—
545#41—34no—
546#41—34no—
547#41—32no—
548#41—32no—
549#41—64no—
550#41—64no—
551#41—64no—
552#41—64no—
553#41—62no—
554#41—62no—
555#41—61no—
556#41—61no—
557#41C2×C4×D312yes—
558#41D3×Q812yes—
559C2×Q8—34no—
560C2×Q8—31no—
561C2×Q8—61no—
562C2×Q8—62no—
563C2×Q8D3×D411yescharacteristic
564C2×D4—21no—
565C2×D4—34no—
566C2×D4—31no—
567C2×D4—61no—
568C2×D4—62no—
569C2×D4—61no—
570C2×D4—64no—
571C2×D4—64no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4D3×D411yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—31no—
579C22×C4—32no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—32no—
585C22×C4—32no—
586C22×C4—32no—
587C22×C4—64no—
588C22×C4—61no—
589C22×C4—64no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—121no—
596C22×C4—121no—
597C22×C4—242no—
598C22×C4C23×D311yescharacteristic
599M16—21no—
600M16—24no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—34no—
606M16—34no—
607M16—34no—
608M16—34no—
609M16—32no—
610M16—64no—
611M16—64no—
612M16—64no—
613M16—61no—
614M16—64no—
615M16—61no—
616M16—61no—
617M16—61no—
618M16—61no—
619M16—122no—
620M16—122no—
621M16C2×C4×D312yes—
622C2×C8—21no—
623C2×C8—24no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—32no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—32no—
630C2×C8—64no—
631C2×C8—64no—
632C2×C8—64no—
633C2×C8—61no—
634C2×C8—64no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—122no—
638C2×C8—122no—
639C2×C8C2×C4×D312yes—
640C2×C8D3×D411yescharacteristic
641C2×C8D3×D411yescharacteristic
642C2×C8D3×D412yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—121no—
652C4⋊C4—121no—
653C22⋊C4—121no—
654C22⋊C4—121no—
655C42—121no—
656C42—121no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3C2×#11711yescharacteristic
663C22×C3C2×#12111yescharacteristic
664C22×C3C2×C22⋊Q811yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—22no—
670C2×D3—42no—
671C2×D3—42no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—84no—
675C2×D3#38012yes—
676C2×D3#38012yes—
677C3×C4—22no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4C22×C22⋊C411yescharacteristic
681C3×C4C22×C4⋊C411yescharacteristic
682C3×C4C2×#12111yescharacteristic
683C3×C4C2×C22⋊Q811yescharacteristic
684Dic3—22no—
685Dic3—81no—
686Dic3—81no—
687Dic3#38012yes—
688Dic3#38012yes—
689C23—21no—
690C23—31no—
691C23—31no—
692C23—32no—
693C23—32no—
694C23—64no—
695C23—61no—
696C23—121no—
697C23—121no—
698C23—241no—
699C23—241no—
700C23D3×#4111yescharacteristic
701Q8—21no—
702Q8—32no—
703Q8—64no—
704Q8—61no—
705Q8D3×C4⋊C412yes—
706D4—22no—
707D4—22no—
708D4—21no—
709D4—32no—
710D4—64no—
711D4—64no—
712D4—64no—
713D4—62no—
714D4—62no—
715D4—61no—
716D4D3×C4⋊C412yes—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—32no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—64no—
735C2×C4—64no—
736C2×C4—64no—
737C2×C4—61no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—242no—
745C2×C4—242no—
746C2×C4—241no—
747C2×C4—241no—
748C2×C4C22×C4×D311yescharacteristic
749C2×C4C2×D3×D411yescharacteristic
750C2×C4C2×D3×D411yescharacteristic
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×D3×Q811yescharacteristic
753C2×C4D3×#4111yescharacteristic
754C8—22no—
755C8—32no—
756C8—32no—
757C8—41no—
758C8—41no—
759C8—62no—
760C8—121no—
761C8—121no—
762C8D3×C22⋊C412yes—
763C8D3×C22⋊C412yes—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3C2×#38011yescharacteristic
768C2×C3#306811yescharacteristic
769C2×C3#306911yescharacteristic
770D3—22no—
771D3—22no—
772D3—42no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—32no—
777C22—32no—
778C22—41no—
779C22—41no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—62no—
785C22—122no—
786C22—122no—
787C22—121no—
788C22—121no—
789C22—244no—
790C22D3×#11711yescharacteristic
791C22D3×#12111yescharacteristic
792C22D3×C22⋊Q811yescharacteristic
793C4—22no—
794C4—32no—
795C4—32no—
796C4—62no—
797C4—81no—
798C4—81no—
799C4—241no—
800C4—241no—
801C4C2×D3×C22⋊C411yescharacteristic
802C4C2×D3×C4⋊C411yescharacteristic
803C4D3×#12111yescharacteristic
804C4D3×C22⋊Q811yescharacteristic
805C3#2067911yescharacteristic, complemented, Sylow
806C2—21no—
807C2—21no—
808C2—42no—
809C2—62no—
810C2—62no—
811C2—122no—
812C2D3×#38011yescharacteristic
813C2#8093011yescharacteristic
814C2#8093111yescharacteristic
subgroupG/H
centerC22D3×#121
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1815C2
socleC22×C3C2×#121
prime radicalC2×D3×#41C22
cosocleC22×C3×C4C24
hypercenter#1815D3
hypocenterC3#20679
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1815

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#4893C2semidirect
3. C2×#4861C2semidirect
6. C3×#1815C2semidirect
7. #72016C2semidirect
8. #70721C2semidirect
9. #70592C2semidirect
10. #70300C2semidirect
11. #70299C2semidirect
12. #69001C2semidirect
13. #69000C2semidirect
14. #68989C2semidirect
15. D3×#343C2semidirect
21. #5750C4semidirect
34. C2×C3×#108C22semidirect
35. C2×C3×#106C22semidirect
42. C2×#822C22semidirect
43. C2×#822C22semidirect
44. C2×#819C22semidirect
45. C2×#818C22semidirect
48. C2×#808C22semidirect
49. C2×#807C22semidirect
63. C3×#343C22semidirect
64. C3×#343C22semidirect
65. #4554C22semidirect
66. #4554C22semidirect
67. #4554C22semidirect
68. #4554C22semidirect
69. #4530C22semidirect
70. #4530C22semidirect
83. #1815D3semidirect
103. C3×#131C2×C4semidirect
113. #948C2×C4semidirect
127. #907C2×C4semidirect
137. #901C2×C4semidirect
212. C2×#108C2×D3semidirect
220. C2×#106C2×D3semidirect
243. #343C2×D3semidirect
244. #343C2×D3semidirect
386. #131C4×D3semidirect
805. C3#20679semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#57502
C2×#48932
C2×#48612
#788812
D3×#4172
C3×#18152
#720162
#707212
#705922
#703002
#702992
#690012
#690002
#689892
D3×#3432
#206793